Consider an industry where firms use a technology that results in the following cost structure for each firm: The first 25 units of output are produced at a constant marginal cost of 3. For any additional units in excess of 25, the marginal cost is lower at 2. There are no fixed costs. MC(y) S3 if y 25 The inverse demand function is Pp(y) = 10 - toy a) Write down the firm's cost function c(y) and the average costs AC(y). (Note: These will be a two-part definitions similar to that of the marginal costs.) Draw the demand curve, the marginal cost curve of a firm (supply curve), the average cost curve and the marginal revenue curve that a monopolist might be interested in. b) Find the market equilibrium if the market is supplied by a single firm that behaves competitively. Calculate price, quantity, the firm's profit, consumer surplus and producer surplus. c) Find the market equilibrium if the market is supplied by two firms that behave competitively and each supply half of the market. Calculate price, quantity, the two firms' profit, consumer surplus and producer surplus. d) Find the market equilibrium if the market is supplied by n > 4 firms that behave competitively and each supply a share of the market. Calculate price, quantity, the combined profit of the n firms, consumer surplus and producer surplus, where relevant as a function of n. Consider an industry where firms use a technology that results in the following cost structure for each firm: The first 25 units of output are produced at a constant marginal cost of 3. For any additional units in excess of 25, the marginal cost is lower at 2. There are no fixed costs. MC(y) S3 if y 25 The inverse demand function is Pp(y) = 10 - toy a) Write down the firm's cost function c(y) and the average costs AC(y). (Note: These will be a two-part definitions similar to that of the marginal costs.) Draw the demand curve, the marginal cost curve of a firm (supply curve), the average cost curve and the marginal revenue curve that a monopolist might be interested in. b) Find the market equilibrium if the market is supplied by a single firm that behaves competitively. Calculate price, quantity, the firm's profit, consumer surplus and producer surplus. c) Find the market equilibrium if the market is supplied by two firms that behave competitively and each supply half of the market. Calculate price, quantity, the two firms' profit, consumer surplus and producer surplus. d) Find the market equilibrium if the market is supplied by n > 4 firms that behave competitively and each supply a share of the market. Calculate price, quantity, the combined profit of the n firms, consumer surplus and producer surplus, where relevant as a function of n
